A New Hardy–Hilbert-Type Integral Inequality Involving General Homogeneous Kernel and Two Derivative Functions of Higher Order

Bicheng Yang, Shanhe Wu () and Xianyong Huang
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Xianyong Huang: School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Mathematics, 2025, vol. 13, issue 21, 1-12

Abstract: In this paper, by introducing a general homogeneous kernel function and several parameters, we establish a new Hardy–Hilbert-type integral inequality involving two derivative functions of higher-order. For the resulting inequality, we determine the equivalent conditions of the best possible constant factor related to the parameters. As applications, we demonstrate that a lot of new Hardy–Hilbert-type integral inequalities can be derived by choosing specific homogeneous kernel functions.

Keywords: Hardy–Hilbert-type integral inequality; general homogeneous kernel function; higher-order derivative function; best possible constant factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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